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How did Pythagoreans associate the numbers 2 and 3 with female and male principles?

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Marble bust of Pythagoras, the ancient Greek mathematician and philosopher, showing a bearded man with a head covering and calm expression. — Pythagoreanism Greek philosopher and mathematician Pythagoras, portrait bust.

In Pythagoreanism, the association of numbers with gendered principles was rooted in the school's broader doctrine of opposites. Within this framework, the Pythagoreans categorized all numbers as either even or odd, assigning them specific symbolic qualities.1

The number 2 was identified as the female principle, representing the unlimited or even, while the number 3 was identified as the male principle, representing the limit or odd. This dualistic classification extended to a "table of ten opposites," which included pairs such as male-female, odd-even, and limit-unlimited.213

These principles were considered fundamental to the structure of the cosmos. The Pythagoreans believed that these opposites "fit together" to create harmony and order. This union was symbolically expressed through the number 5, which was formed by the addition of the female 2 and the male 3, representing marriage.241